Lemma 1. [1]} Let \((X;m)\)  be a measure space,
\(\mathcal {F}(X)\) 
some Banach space of \(m\) -measurable functions on \(X\) , \((\Omega ,\mu )\)  a \(\sigma \) -compact quasi-metric space with positive Radon measure \(\mu \) , and \(F(w, z)\)  a function on \(\Omega \times X\) . Assume that
